(CNN)A Democratic senator said Tuesday that his conservative constituents are warming to the idea of universal government-run insurance, which has long been a policy goal of progressives.

"What I'm hearing -- even in these conservative parts of my state that I lost by 30, 40% when I was running for re-election -- what I'm hearing is the system is way too stressful," Sen. Jeff Merkley told CNN's Alisyn Camerota during a discussion on health care legislation on "New Day." "I've been asking each audience, I've been saying, 'How many people here 10 years ago would have supported a single-payer Medicare-for-all?' And it's a small number. And then I ask, 'How many now?' And the hands just go up throughout the room."

Merkley added, "People are so stressed about the complexity and difficulty of our health care system. Can't we make this simpler?"

Merkley's Republican colleagues in Congress, however, have given no indication that they would consider legislation to create a single-payer health insurance program. Senate Majority Leader Mitch McConnell said Tuesday that a single-payer health care plan similar to the one championed by Sen. Bernie Sanders during his presidential campaign "would strip Americans of so many facets of decision-making over their own health-care and hand it to the government."

Merkley was on "New Day" to discuss the Senate GOP's health care bill, which includes proposals to eliminate the taxes imposed on high-income Americans to help pay for an expansion of health benefits under the Affordable Care Act.